Details

analyze528.0ms (10.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
12.5%	50%	37.5%	4
18.7%	37.5%	43.8%	5
21.9%	31.2%	46.9%	6
21.9%	29.7%	48.5%	7
21.9%	28.9%	49.2%	8
22.3%	28.1%	49.6%	9
22.3%	27.9%	49.8%	10
22.3%	27.8%	49.9%	11
22.4%	27.7%	50%	12
22.4%	27.6%	50%	13
22.4%	27.6%	50%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.7s (33.8%)

Results

716.0ms	2043×	body	1024	valid
445.0ms	4389×	body	128	valid
291.0ms	1058×	body	512	valid
103.0ms	256×	body	2048	valid
89.0ms	510×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

prune44.0ms (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

32.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	32.7b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.6b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series18.0ms (0.4%)

Counts

1 → 1

Calls

1 calls:

18.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`sqrt-prod_binary64`
52×	`*-un-lft-identity_binary64`
42×	`prod-diff_binary64`
39×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`

Counts

1 → 75

Calls

1 calls:

8.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify176.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

485×	`sqr-pow_binary64`
481×	`fma-neg_binary64`
455×	`unsub-neg_binary64`
425×	`unswap-sqr_binary64`
380×	`exp-prod_binary64`

Counts

76 → 69

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	87	2325
1	154	1099
2	417	889
3	1547	889
4	3056	889
5	4410	889
6	4523	889
7	4696	853
8	4047	853
9	4796	853
10	4713	853

prune75.0ms (1.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	2	70

Error

0.1b

Counts

70 → 2

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	32.7b	(+.f64 (sqrt.f64 (+.f64 x 1)) (*.f64 (neg.f64 1) (sqrt.f64 x)))

Compiler

Compiled 1534 to 764 computations (50.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series24.0ms (0.5%)

Counts

2 → 2

Calls

2 calls:

14.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
15×	`add-sqr-sqrt_binary64`

Counts

2 → 70

Calls

2 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
6.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify128.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

744×	`div-sub_binary64`
483×	`fma-neg_binary64`
334×	`times-frac_binary64`
317×	`associate-/l*_binary64`
310×	`distribute-rgt-in_binary64`

Counts

72 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	1097
1	123	1012
2	243	1012
3	504	1010
4	1190	1010
5	2283	1010
6	4202	1010
7	4971	1010
8	4998	1010
9	4828	1010

prune103.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	62	5	67
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	63	6	69

Error

0.0b

Counts

69 → 6

Alt Table

Status	Error	Program
	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	9.9b	(cbrt.f64 (.f64 (.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.8b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	10.0b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
▶	0.3b	(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))

Compiler

Compiled 1426 to 1027 computations (28% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (+.f64 1 x)))
✓	0.2b	(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
✓	0.3b	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
✓	0.3b	(cbrt.f64 (+.f64 1 x))

series118.0ms (2.4%)

Counts

4 → 37

Calls

4 calls:

100.0ms	(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
8.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
6.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 x)))
5.0ms	(cbrt.f64 (+.f64 1 x))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
33×	`cbrt-prod_binary64`
23×	`add-cube-cbrt_binary64`
16×	`cbrt-div_binary64`

Counts

4 → 127

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
6.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 x)))
2.0ms	(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
2.0ms	(cbrt.f64 (+.f64 1 x))

simplify158.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

585×	`fma-def_binary64`
551×	`fma-neg_binary64`
318×	`associate-l_binary64`
292×	`associate-r_binary64`
213×	`unswap-sqr_binary64`

Counts

164 → 221

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	240	3489
1	533	3077
2	1298	2765
3	3736	2476
4	4812	2476
5	4977	2415
6	4874	2415

prune446.0ms (9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	305	0	305
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	305	6	311

Error

0.0b

Counts

311 → 6

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	9.9b	(cbrt.f64 (.f64 (.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.8b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	10.0b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
✓	0.3b	(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))

Compiler

Compiled 9090 to 6951 computations (23.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

series52.0ms (1%)

Counts

2 → 2

Calls

2 calls:

38.0ms

(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

14.0ms

(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite85.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`sqrt-prod_binary64`
236×	`*-un-lft-identity_binary64`
148×	`times-frac_binary64`
144×	`add-sqr-sqrt_binary64`
84×	`distribute-lft-out_binary64`

Counts

2 → 204

Calls

2 calls:

34.0ms

(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

8.0ms

(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

simplify231.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

635×	`unswap-sqr_binary64`
539×	`times-frac_binary64`
411×	`div-sub_binary64`
403×	`fma-def_binary64`
378×	`associate-/l*_binary64`

Counts

206 → 200

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	111	4253
1	186	4015
2	493	3961
3	1230	3833
4	2521	3833
5	4243	3833
6	4256	3829
7	4926	3829
8	4788	3829

prune494.0ms (9.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	372	3	375
Fresh	2	1	3
Picked	0	1	1
Done	1	1	2
Total	375	6	381

Error

Counts

381 → 6

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.6b	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4) (/.f64 -1 2))
	0.4b	(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 -1 2))
	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
	10.0b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
✓	0.3b	(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))

Compiler

Compiled 11265 to 8323 computations (26.1% saved)

regimes377.0ms (7.6%)

Accuracy

Total 0.1b remaining (83.7%)

Threshold costs 0.1b (83.7%)

Counts

184 → 1

Compiler

Compiled 8529 to 6654 computations (22% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	12	14
2	11	14

end121.0ms (2.4%)

Compiler: Compiled 170 to 130 computations (23.5% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Details

analyze528.0ms (10.6%)

sample1.7s (33.8%)

simplify11.0ms (0.2%)

prune44.0ms (0.9%)

localize5.0ms (0.1%)

series18.0ms (0.4%)

rewrite16.0ms (0.3%)

simplify176.0ms (3.6%)

prune75.0ms (1.5%)

localize6.0ms (0.1%)

series24.0ms (0.5%)

rewrite21.0ms (0.4%)

simplify128.0ms (2.6%)

prune103.0ms (2.1%)

localize10.0ms (0.2%)

series118.0ms (2.4%)

rewrite26.0ms (0.5%)

simplify158.0ms (3.2%)

prune446.0ms (9%)

localize9.0ms (0.2%)

series52.0ms (1%)

rewrite85.0ms (1.7%)

simplify231.0ms (4.7%)

prune494.0ms (9.9%)

regimes377.0ms (7.6%)

simplify2.0ms (0%)

end121.0ms (2.4%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11